She is 17 years old, and is a student at a prestigious Catholic high school which this week opened its gymnasium as a temporary shelter for dozens of families who lost everything in the magnitude 7.1 quake.

Armed with little more than a clipboard and the can-do attitude that has come to define the post-disaster civilian response, Villar directs a delivery of sandwiches and cakes donated by a local bakery to tables flanking neat rows of blue exercise mats laid out as mattresses on the polished gym floor.

Moving quickly on, the teenager asks a volunteer psychologist to attend to a distraught woman who has just arrived after her building was declared uninhabitable.

In another corner, clowns and face painters entertain the children so their parents can rest or sort through donated clothes in hope of finding something that will fit them.

“There are more volunteers than victims because everyone wants to help,” said Villar. “Mexico has united and we won’t stop while people are suffering because we feel their pain too.”

Therapists and psychologists offer their support to families whose houses were damaged during the quake and cannot return home, in Mexico City on Friday. Photograph: Alfredo Estrella/AFP/Getty Images

The civic response to the earthquake – the second to hit the country within two weeks – has been extraordinary.

As soon as the earth stopped trembling on Tuesday, people sprang into action to shift debris with their bare hands and carry the injured to safety.

By the following day, ordinary Mexicans had created a vast recovery operation to fill every imaginable gap in the official response. Donation sites were set up to receive, organise and deliver essential supplies of food, water, medicines, bedding, clothes and tools to rescue sites and shelters. In many cases, search and rescue operations continued throughout the night thanks to lamps, batteries and petrol donated by members of the public.

The huge army of volunteers established spontaneous networks, using cars, trucks, motorcycles and bikes to access even the most isolated zones not yet reached by authorities. Engineers, doctors, vets, therapists, couriers and cooks contributed specialist skills and equipment. Taco vendors donated food to rescuers.

The last time Mexico saw a civilian mobilisation on such a scale was in 1985 after the country’s deadliest quake killed thousands and flattened large parts of the capital.

Then, the government was criticised for its slow, inadequate response. The omnipresent issue of corruption was blamed for widespread violations of building codes that contributed to the devastation.

Enrique Peña Nieto, the most unpopular president in Mexico’s recent history, has been at pains to praise the public response as evidence of the country’s unity and greatness. But cracks between the state and civilian responses are now opening amid mounting scrutiny of the official narrative.

While many volunteers are too young to remember the 1985 quake, 48-year-old Kudilma López, a psychotherapist who is here in the Colonia del Valle neighbourhood with her Jeep to deliver supplies and people, remembers it well.

“We responded immediately this time like we did in 1985, because the government is very slow and badly organised. By the time its institutions turn up and want to take over, the people have already organised and this can cause problems,” she said.

The armed forces, which have taken control of most search and rescue operations after the initial ad hoc civilian efforts, have been lambasted for allegedly trying to raze collapsed buildings even though rescue brigades want to continue searching for survivors.

On Friday morning, citizens prevented bulldozers from entering the site of a ruined clothes factory in the city’s Obrera neighbourhood, allowing a rescue brigade to continue searching for several workers believed to be buried under the rubble.

Frida Sofía, age 12: the Mexico City quake 'survivor' who was never there

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On Thursday, the navy was forced to apologise for its part in the media circus surrounding the supposedly imminent rescue of a 12-year-old girl from the ruins of a school. After several days of breathless television coverage, the navy admitted that there was no evidence that the girl – named Frida Sofía – had ever existed.

But as security forces assert control in all the affected states, accusations of corruption and mismanagement are circulating amid fears that truckloads of food and medicines could be redirected away from the communities that need them by criminals or political parties.

Last month outrage erupted after the National Electoral Institute (INE) approved a record-breaking £280m ($378m/6,778m pesos) of public money to finance the widely distrusted political parties and independent candidates in 2018, a general election year.

Nevertheless, victims of the quake are worried about how they will survive once the shelters close and volunteers return to their normal lives.

Sergio Árias Rodríguez, 44, his wife, Teresa Gonzales, 41, and their 16-year-old son were the first to arrive at the Del Valle shelter on Tuesday after their 13-storey apartment block collapsed like a house of cards.

The couple work as street vendors, walking the city selling sweets, cigarettes and snacks, and earning about £13 each day. The family lost everything – including their savings which they kept hidden at home as neither has a bank account.

“We’re so grateful because we’re alive, and for all the help and solidarity we’ve received here. It feels like we’re among family, but what happens next? We’re starting again from zero,” said Rodríguez, who is looking for cheap hotel rooms to move his family into next week when the school reopens.

“The government says it will help people like us who lost everything, but we can’t count on that. So, on Monday we’ll go back to work and start rebuilding our lives.”